I have fitted an exponential model to some data using maximum likelihood estimation and am now trying to compute a prediction interval for a new observation, $P$, which has a corresponding explanatory variable equal to $70$.
Under my model, $P \sim \text{Exp}(e^{\beta_1 + \beta_2 \times 70})$ and I have estimated $\hat{\beta}_1 = -4.317$ and $\hat{\beta}_2 = -0.028$. Further, the inverse observed fisher information for the model is:
$$-H(\boldsymbol{\hat{\theta}})^{-1} = \begin{bmatrix} 0.615 & -0.009 \\ -0.009 & 0.00017 \end{bmatrix}$$
My question is, how can I create a $95\%$ prediction interval for $P$ using this information?